微积分

I spent the last week in China and Taiwan doing two workshops for AP Calculus teachers for the College Board. It was an interesting and fun trip for me.

To get to China from Dallas you fly due north almost to the North Pole and then turn left and fly south over Siberia, Mongolia, and into China.

Siberia from 37,000 feet looking east

Siberia from 37,000 feet looking west

The flight took 15 hours. In Shanghai I met the others in our group. Shanghai is a modern city of over 14 million people. There are many tall office buildings and apartment houses. Driving in from the airport in the evening I was struck by how dark the city appeared. The office workers had gone home and all the office lights were out. Neither the offices nor the apartments had the outside lighting so everything looked dark. There were many cars and of course the resulting traffic jams. Electric motor scooters were popular.We spent the next day sightseeing and shopping and resting.

Our first workshop was in Suzhou a city of 4.3 million a two-hour drive west from Shanghai. Actually, the two cities sort of run together with little open land between them. We toured the old part of the city – an area connected by narrow canals and bridges.

Then we continued another hour to the modern part of the city and got down to work setting up our classrooms and getting organized.

The two-day workshops started the next morning. The sessions were held at the Suzhou Foreign Language School, a K – 12 boarding school. The participants were teachers from all over China who, for the most part, were planning to teach AP next year. We had over 270 participants in AP Calculus, Economics, English Language and Composition, Geography, Psychology, Statistics, and pre-AP English, and an additional session for administrators. Most of the participants were Chinese teachers, the others were ex-pats from several countries teaching in China all with a good command of English.

My calculus group at the workshop

My session was one of two in AP Calculus. The other was led by Tim Zitur, an American living in Singapore, who is an experienced table leader and workshop leader. The sessions were conducted in English which all of the participant understood. The questions and discussions were very much the same as any workshop in the USA.

Students in China take AP courses so that they can apply to schools in the USA. In China, students take one test before they apply to college. Talk about high-stakes testing: a high score on the exam allows them to apply to the best colleges in China; a lower score prohibits them from applying to the best colleges. A difference of one point can move over 100,000 students from one category to the other. To avoid this, students whose families can afford it send their child to a school in America and use AP credit help then get accepted here.

We were always made to feel welcome. The school took the presenters to a very nice restaurant on the fourth floor of a local mall (you’d recognize a lot of the stores) where we had a Chinese dinner of about two-dozen courses! We all sat at a round table with a huge lazy-Susan as the dishes went around.

After the second day we were driven back to Shanghai; everyone fell asleep on the two-hour trip.

The next morning we were up early for a flight to Taiwan for our next meeting in Taichung. Taichung is a two-hour ride from the airport in Taipei. It is the third largest city in Taiwan with a population of 2.6 million.

The night we arrived we visited the Taichung Lantern Festival. The Chinese New Year’s season was in full swing. We entered what looked like a typical American fair – lots of small booths each serving a different kind of food. Then we headed to the display area. There were acres and acres of large colorful figures made of cloth stretched over heavy wire frames and lit from the inside with colored lights. Beautiful and difficult to describe. Notice the size of the people silhouetted in the pictures below.

Food at the Taichung Lantern Festival

It is the Year of the Ram

Taichung Lantern Festival

Taichung Lantern Festival

There were thousands of people of all ages in attendance, yet I saw no one smoking and there was not a bit of trash or litter on the ground.

Our meetings the next day were at the National Taichung Girls’ Senior High School. The purpose of this meeting was to introduce Advanced Placement to the teachers and administrators. The plenary sessions were in Chinese. While they were going on Tai Hus-Chang, the principal of the school, showed us around. The classes had over 40 girls each. The girls stay in the rooms and the teachers move from class to class. The pupils were very eager to speak to us and spoke very good English.

Students from the National Taichung Girls’ High School with Tai Hsu-Chang, the principal, me, and Marty Sternstein, the AP Statistics presenter.

I had a look at an eleventh grade math textbook. The book was in Chinese of course. It included solid geometry, the three-dimensional equations of lines, solving systems of three equations by determinants (in the context of the intersection of planes), matrices (including translations and rotation matrices), and a complete chapter on the conic sections. The book had very little text, no sidebars, and very little in the way of pictures not related to the problems. The mathematics was written in standard notation with English letters for the variables.

I lead two breakout sessions. The first for teachers was a quick introduction to AP Calculus. Students joined us for the second breakout session. I taught a demonstration lesson using the Rule of Four and technology to present the average value of a function. Since the “calculus” came only at the end the students seemed to understand what was going on well enough. My translator (for the teachers) was Dr. Bo Wang, vice-president of the College Board and the leader of the trip.

We were treated to another nice dinner by the president of the Parent Teachers Organization: ten delicious courses.

Shrimp

Tuna

Dessert soup

Braised pork

Then the next day was the long trip home. It was quite a trip and interesting to see mathematics, calculus, teachers, and students in another part of the world.